The Rayleigh problem for a slightly diffusive density-stratified fluid

Abstract

A doubly-infinite sloping flat plate, initially at rest in a slightly diffusive viscous density-stratified fluid, starts to move impulsively with a constant velocity along the line of greatest slope. The resulting flow is found to be an unsteady motion superimposed on a steady diffusion-induced flow, which is present throughout. Laplace transform methods give solutions which are valid either in an essentially non-diffusive outer layer or in a diffusive inner layer. The impulsive start sets up oscillations in the outer layer. These gradually die out, and a steady diffusive flow develops.A glass plate was towed vertically through stratified brine, into which aluminium particles were introduced. The flow velocities deduced from the particle motions confirmed the theoretical predictions.